{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 20 × 6 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>X1</th><th scope=col>X2</th><th scope=col>X3</th><th scope=col>Y1</th><th scope=col>Y2</th><th scope=col>Y3</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 0.5022173</td><td> 0.1873845</td><td>-0.84600343</td><td>-0.8418021</td><td> 0.2629199</td><td>-0.2008679</td></tr>\n",
       "\t<tr><td> 0.5832201</td><td> 0.8119993</td><td> 0.26350927</td><td> 0.4823810</td><td>-0.7120415</td><td> 0.5987035</td></tr>\n",
       "\t<tr><td> 0.4212145</td><td>-0.1249230</td><td>-1.40075978</td><td> 0.6715500</td><td> 0.1510391</td><td>-0.2398714</td></tr>\n",
       "\t<tr><td> 1.3122453</td><td> 0.8119993</td><td>-0.01386891</td><td>-0.2742951</td><td>-0.7120415</td><td>-0.6299063</td></tr>\n",
       "\t<tr><td>-0.1053036</td><td>-1.3741527</td><td> 2.48253466</td><td> 1.0498880</td><td> 0.8702730</td><td>-0.5909028</td></tr>\n",
       "\t<tr><td>-0.3888134</td><td>-0.4372304</td><td>-0.84600343</td><td> 1.4282260</td><td>-0.4083650</td><td>-0.6299063</td></tr>\n",
       "\t<tr><td>-0.9963344</td><td>-0.4372304</td><td> 1.09564379</td><td> 0.8607190</td><td> 1.1100176</td><td> 0.6767105</td></tr>\n",
       "\t<tr><td> 0.5832201</td><td> 0.1873845</td><td>-1.40075978</td><td>-0.6526331</td><td>-1.2075138</td><td>-0.7664185</td></tr>\n",
       "\t<tr><td>-0.1053036</td><td> 0.4996919</td><td>-0.29124708</td><td>-1.0309711</td><td>-1.3673435</td><td>-0.8834289</td></tr>\n",
       "\t<tr><td>-0.9153316</td><td>-0.7495378</td><td>-0.29124708</td><td> 1.0498880</td><td> 1.2698474</td><td> 0.0526547</td></tr>\n",
       "\t<tr><td> 0.4212145</td><td> 0.4996919</td><td>-0.56862526</td><td>-1.4093091</td><td>-0.5681948</td><td>-0.2008679</td></tr>\n",
       "\t<tr><td>-0.6723232</td><td>-0.1249230</td><td> 0.81826561</td><td> 0.4823810</td><td>-0.6481096</td><td>-0.6494080</td></tr>\n",
       "\t<tr><td> 0.1377048</td><td> 0.1873845</td><td>-0.01386891</td><td>-1.0309711</td><td>-0.7120415</td><td>-0.5518993</td></tr>\n",
       "\t<tr><td>-0.4698162</td><td>-0.4372304</td><td> 0.54088744</td><td>-0.6526331</td><td>-0.3284501</td><td>-0.5909028</td></tr>\n",
       "\t<tr><td>-0.9963344</td><td>-0.7495378</td><td>-0.01386891</td><td> 1.4282260</td><td> 1.6854047</td><td> 3.5044631</td></tr>\n",
       "\t<tr><td>-0.5103176</td><td>-0.7495378</td><td>-0.56862526</td><td> 0.6715500</td><td> 1.0301027</td><td> 0.8717279</td></tr>\n",
       "\t<tr><td> 2.7702957</td><td> 3.3104588</td><td>-0.84600343</td><td>-1.5984781</td><td>-1.5271733</td><td>-0.3958854</td></tr>\n",
       "\t<tr><td> 0.9477327</td><td> 0.4996919</td><td> 0.81826561</td><td> 0.4823810</td><td> 1.0301027</td><td> 0.9692366</td></tr>\n",
       "\t<tr><td>-0.8748302</td><td>-1.0618453</td><td>-0.56862526</td><td> 0.2932120</td><td> 1.3497622</td><td> 0.1891669</td></tr>\n",
       "\t<tr><td>-1.6443568</td><td>-0.7495378</td><td> 1.65040014</td><td>-1.4093091</td><td>-0.5681948</td><td>-0.5323976</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 20 × 6 of type dbl\n",
       "\\begin{tabular}{llllll}\n",
       " X1 & X2 & X3 & Y1 & Y2 & Y3\\\\\n",
       "\\hline\n",
       "\t  0.5022173 &  0.1873845 & -0.84600343 & -0.8418021 &  0.2629199 & -0.2008679\\\\\n",
       "\t  0.5832201 &  0.8119993 &  0.26350927 &  0.4823810 & -0.7120415 &  0.5987035\\\\\n",
       "\t  0.4212145 & -0.1249230 & -1.40075978 &  0.6715500 &  0.1510391 & -0.2398714\\\\\n",
       "\t  1.3122453 &  0.8119993 & -0.01386891 & -0.2742951 & -0.7120415 & -0.6299063\\\\\n",
       "\t -0.1053036 & -1.3741527 &  2.48253466 &  1.0498880 &  0.8702730 & -0.5909028\\\\\n",
       "\t -0.3888134 & -0.4372304 & -0.84600343 &  1.4282260 & -0.4083650 & -0.6299063\\\\\n",
       "\t -0.9963344 & -0.4372304 &  1.09564379 &  0.8607190 &  1.1100176 &  0.6767105\\\\\n",
       "\t  0.5832201 &  0.1873845 & -1.40075978 & -0.6526331 & -1.2075138 & -0.7664185\\\\\n",
       "\t -0.1053036 &  0.4996919 & -0.29124708 & -1.0309711 & -1.3673435 & -0.8834289\\\\\n",
       "\t -0.9153316 & -0.7495378 & -0.29124708 &  1.0498880 &  1.2698474 &  0.0526547\\\\\n",
       "\t  0.4212145 &  0.4996919 & -0.56862526 & -1.4093091 & -0.5681948 & -0.2008679\\\\\n",
       "\t -0.6723232 & -0.1249230 &  0.81826561 &  0.4823810 & -0.6481096 & -0.6494080\\\\\n",
       "\t  0.1377048 &  0.1873845 & -0.01386891 & -1.0309711 & -0.7120415 & -0.5518993\\\\\n",
       "\t -0.4698162 & -0.4372304 &  0.54088744 & -0.6526331 & -0.3284501 & -0.5909028\\\\\n",
       "\t -0.9963344 & -0.7495378 & -0.01386891 &  1.4282260 &  1.6854047 &  3.5044631\\\\\n",
       "\t -0.5103176 & -0.7495378 & -0.56862526 &  0.6715500 &  1.0301027 &  0.8717279\\\\\n",
       "\t  2.7702957 &  3.3104588 & -0.84600343 & -1.5984781 & -1.5271733 & -0.3958854\\\\\n",
       "\t  0.9477327 &  0.4996919 &  0.81826561 &  0.4823810 &  1.0301027 &  0.9692366\\\\\n",
       "\t -0.8748302 & -1.0618453 & -0.56862526 &  0.2932120 &  1.3497622 &  0.1891669\\\\\n",
       "\t -1.6443568 & -0.7495378 &  1.65040014 & -1.4093091 & -0.5681948 & -0.5323976\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 20 × 6 of type dbl\n",
       "\n",
       "| X1 | X2 | X3 | Y1 | Y2 | Y3 |\n",
       "|---|---|---|---|---|---|\n",
       "|  0.5022173 |  0.1873845 | -0.84600343 | -0.8418021 |  0.2629199 | -0.2008679 |\n",
       "|  0.5832201 |  0.8119993 |  0.26350927 |  0.4823810 | -0.7120415 |  0.5987035 |\n",
       "|  0.4212145 | -0.1249230 | -1.40075978 |  0.6715500 |  0.1510391 | -0.2398714 |\n",
       "|  1.3122453 |  0.8119993 | -0.01386891 | -0.2742951 | -0.7120415 | -0.6299063 |\n",
       "| -0.1053036 | -1.3741527 |  2.48253466 |  1.0498880 |  0.8702730 | -0.5909028 |\n",
       "| -0.3888134 | -0.4372304 | -0.84600343 |  1.4282260 | -0.4083650 | -0.6299063 |\n",
       "| -0.9963344 | -0.4372304 |  1.09564379 |  0.8607190 |  1.1100176 |  0.6767105 |\n",
       "|  0.5832201 |  0.1873845 | -1.40075978 | -0.6526331 | -1.2075138 | -0.7664185 |\n",
       "| -0.1053036 |  0.4996919 | -0.29124708 | -1.0309711 | -1.3673435 | -0.8834289 |\n",
       "| -0.9153316 | -0.7495378 | -0.29124708 |  1.0498880 |  1.2698474 |  0.0526547 |\n",
       "|  0.4212145 |  0.4996919 | -0.56862526 | -1.4093091 | -0.5681948 | -0.2008679 |\n",
       "| -0.6723232 | -0.1249230 |  0.81826561 |  0.4823810 | -0.6481096 | -0.6494080 |\n",
       "|  0.1377048 |  0.1873845 | -0.01386891 | -1.0309711 | -0.7120415 | -0.5518993 |\n",
       "| -0.4698162 | -0.4372304 |  0.54088744 | -0.6526331 | -0.3284501 | -0.5909028 |\n",
       "| -0.9963344 | -0.7495378 | -0.01386891 |  1.4282260 |  1.6854047 |  3.5044631 |\n",
       "| -0.5103176 | -0.7495378 | -0.56862526 |  0.6715500 |  1.0301027 |  0.8717279 |\n",
       "|  2.7702957 |  3.3104588 | -0.84600343 | -1.5984781 | -1.5271733 | -0.3958854 |\n",
       "|  0.9477327 |  0.4996919 |  0.81826561 |  0.4823810 |  1.0301027 |  0.9692366 |\n",
       "| -0.8748302 | -1.0618453 | -0.56862526 |  0.2932120 |  1.3497622 |  0.1891669 |\n",
       "| -1.6443568 | -0.7495378 |  1.65040014 | -1.4093091 | -0.5681948 | -0.5323976 |\n",
       "\n"
      ],
      "text/plain": [
       "      X1         X2         X3          Y1         Y2         Y3        \n",
       " [1,]  0.5022173  0.1873845 -0.84600343 -0.8418021  0.2629199 -0.2008679\n",
       " [2,]  0.5832201  0.8119993  0.26350927  0.4823810 -0.7120415  0.5987035\n",
       " [3,]  0.4212145 -0.1249230 -1.40075978  0.6715500  0.1510391 -0.2398714\n",
       " [4,]  1.3122453  0.8119993 -0.01386891 -0.2742951 -0.7120415 -0.6299063\n",
       " [5,] -0.1053036 -1.3741527  2.48253466  1.0498880  0.8702730 -0.5909028\n",
       " [6,] -0.3888134 -0.4372304 -0.84600343  1.4282260 -0.4083650 -0.6299063\n",
       " [7,] -0.9963344 -0.4372304  1.09564379  0.8607190  1.1100176  0.6767105\n",
       " [8,]  0.5832201  0.1873845 -1.40075978 -0.6526331 -1.2075138 -0.7664185\n",
       " [9,] -0.1053036  0.4996919 -0.29124708 -1.0309711 -1.3673435 -0.8834289\n",
       "[10,] -0.9153316 -0.7495378 -0.29124708  1.0498880  1.2698474  0.0526547\n",
       "[11,]  0.4212145  0.4996919 -0.56862526 -1.4093091 -0.5681948 -0.2008679\n",
       "[12,] -0.6723232 -0.1249230  0.81826561  0.4823810 -0.6481096 -0.6494080\n",
       "[13,]  0.1377048  0.1873845 -0.01386891 -1.0309711 -0.7120415 -0.5518993\n",
       "[14,] -0.4698162 -0.4372304  0.54088744 -0.6526331 -0.3284501 -0.5909028\n",
       "[15,] -0.9963344 -0.7495378 -0.01386891  1.4282260  1.6854047  3.5044631\n",
       "[16,] -0.5103176 -0.7495378 -0.56862526  0.6715500  1.0301027  0.8717279\n",
       "[17,]  2.7702957  3.3104588 -0.84600343 -1.5984781 -1.5271733 -0.3958854\n",
       "[18,]  0.9477327  0.4996919  0.81826561  0.4823810  1.0301027  0.9692366\n",
       "[19,] -0.8748302 -1.0618453 -0.56862526  0.2932120  1.3497622  0.1891669\n",
       "[20,] -1.6443568 -0.7495378  1.65040014 -1.4093091 -0.5681948 -0.5323976"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$cor</dt>\n",
       "\t\t<dd><style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>0.795608154419992</li><li>0.200556041107123</li><li>0.0725702862103672</li></ol>\n",
       "</dd>\n",
       "\t<dt>$xcoef</dt>\n",
       "\t\t<dd><table>\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td>-0.17788841</td><td>-0.43230348</td><td>-0.04381432</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td> 0.36232695</td><td> 0.27085764</td><td> 0.11608883</td></tr>\n",
       "\t<tr><th scope=row>X3</th><td>-0.01356309</td><td>-0.05301954</td><td> 0.24106633</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$ycoef</dt>\n",
       "\t\t<dd><table>\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Y1</th><td>-0.08018009</td><td>-0.08615561</td><td>-0.29745900</td></tr>\n",
       "\t<tr><th scope=row>Y2</th><td>-0.24180670</td><td> 0.02833066</td><td> 0.28373986</td></tr>\n",
       "\t<tr><th scope=row>Y3</th><td> 0.16435956</td><td> 0.24367781</td><td>-0.09608099</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$xcenter</dt>\n",
       "\t\t<dd><style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>X1</dt><dd>2.28983498828939e-16</dd><dt>X2</dt><dd>4.3159920082303e-16</dd><dt>X3</dt><dd>-1.77895892461422e-16</dd></dl>\n",
       "</dd>\n",
       "\t<dt>$ycenter</dt>\n",
       "\t\t<dd><style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>Y1</dt><dd>1.47104550762833e-16</dd><dt>Y2</dt><dd>-1.77635683940025e-16</dd><dt>Y3</dt><dd>4.9960036108132e-17</dd></dl>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$cor] \\begin{enumerate*}\n",
       "\\item 0.795608154419992\n",
       "\\item 0.200556041107123\n",
       "\\item 0.0725702862103672\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\item[\\$xcoef] A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "\tX1 & -0.17788841 & -0.43230348 & -0.04381432\\\\\n",
       "\tX2 &  0.36232695 &  0.27085764 &  0.11608883\\\\\n",
       "\tX3 & -0.01356309 & -0.05301954 &  0.24106633\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$ycoef] A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "\tY1 & -0.08018009 & -0.08615561 & -0.29745900\\\\\n",
       "\tY2 & -0.24180670 &  0.02833066 &  0.28373986\\\\\n",
       "\tY3 &  0.16435956 &  0.24367781 & -0.09608099\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$xcenter] \\begin{description*}\n",
       "\\item[X1] 2.28983498828939e-16\n",
       "\\item[X2] 4.3159920082303e-16\n",
       "\\item[X3] -1.77895892461422e-16\n",
       "\\end{description*}\n",
       "\n",
       "\\item[\\$ycenter] \\begin{description*}\n",
       "\\item[Y1] 1.47104550762833e-16\n",
       "\\item[Y2] -1.77635683940025e-16\n",
       "\\item[Y3] 4.9960036108132e-17\n",
       "\\end{description*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$cor\n",
       ":   1. 0.795608154419992\n",
       "2. 0.200556041107123\n",
       "3. 0.0725702862103672\n",
       "\n",
       "\n",
       "\n",
       "$xcoef\n",
       ":   \n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| X1 | -0.17788841 | -0.43230348 | -0.04381432 |\n",
       "| X2 |  0.36232695 |  0.27085764 |  0.11608883 |\n",
       "| X3 | -0.01356309 | -0.05301954 |  0.24106633 |\n",
       "\n",
       "\n",
       "$ycoef\n",
       ":   \n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| Y1 | -0.08018009 | -0.08615561 | -0.29745900 |\n",
       "| Y2 | -0.24180670 |  0.02833066 |  0.28373986 |\n",
       "| Y3 |  0.16435956 |  0.24367781 | -0.09608099 |\n",
       "\n",
       "\n",
       "$xcenter\n",
       ":   X1\n",
       ":   2.28983498828939e-16X2\n",
       ":   4.3159920082303e-16X3\n",
       ":   -1.77895892461422e-16\n",
       "\n",
       "\n",
       "$ycenter\n",
       ":   Y1\n",
       ":   1.47104550762833e-16Y2\n",
       ":   -1.77635683940025e-16Y3\n",
       ":   4.9960036108132e-17\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$cor\n",
       "[1] 0.79560815 0.20055604 0.07257029\n",
       "\n",
       "$xcoef\n",
       "          [,1]        [,2]        [,3]\n",
       "X1 -0.17788841 -0.43230348 -0.04381432\n",
       "X2  0.36232695  0.27085764  0.11608883\n",
       "X3 -0.01356309 -0.05301954  0.24106633\n",
       "\n",
       "$ycoef\n",
       "          [,1]        [,2]        [,3]\n",
       "Y1 -0.08018009 -0.08615561 -0.29745900\n",
       "Y2 -0.24180670  0.02833066  0.28373986\n",
       "Y3  0.16435956  0.24367781 -0.09608099\n",
       "\n",
       "$xcenter\n",
       "           X1            X2            X3 \n",
       " 2.289835e-16  4.315992e-16 -1.778959e-16 \n",
       "\n",
       "$ycenter\n",
       "           Y1            Y2            Y3 \n",
       " 1.471046e-16 -1.776357e-16  4.996004e-17 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 20 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>-0.009969788</td><td>-0.121501078</td><td>-0.20419401</td></tr>\n",
       "\t<tr><td> 0.186887139</td><td>-0.046163013</td><td> 0.13223387</td></tr>\n",
       "\t<tr><td>-0.101193522</td><td>-0.141661215</td><td>-0.37063341</td></tr>\n",
       "\t<tr><td> 0.060964112</td><td>-0.346616669</td><td> 0.03342558</td></tr>\n",
       "\t<tr><td>-0.512831098</td><td>-0.458299483</td><td> 0.44354554</td></tr>\n",
       "\t<tr><td>-0.077780541</td><td> 0.094512914</td><td>-0.23766491</td></tr>\n",
       "\t<tr><td> 0.003955674</td><td> 0.254201102</td><td> 0.25701898</td></tr>\n",
       "\t<tr><td>-0.016855040</td><td>-0.127105942</td><td>-0.34147617</td></tr>\n",
       "\t<tr><td> 0.203734347</td><td> 0.196310283</td><td>-0.00758741</td></tr>\n",
       "\t<tr><td>-0.104800666</td><td> 0.208124774</td><td>-0.11711820</td></tr>\n",
       "\t<tr><td> 0.113834968</td><td>-0.016598895</td><td>-0.09752299</td></tr>\n",
       "\t<tr><td> 0.063237343</td><td> 0.213427257</td><td> 0.21221151</td></tr>\n",
       "\t<tr><td> 0.043586465</td><td>-0.008040409</td><td> 0.01237648</td></tr>\n",
       "\t<tr><td>-0.082181602</td><td> 0.055998387</td><td> 0.10021686</td></tr>\n",
       "\t<tr><td>-0.094153311</td><td> 0.228436101</td><td>-0.04670258</td></tr>\n",
       "\t<tr><td>-0.173085857</td><td> 0.047742282</td><td>-0.20173015</td></tr>\n",
       "\t<tr><td> 0.718139369</td><td>-0.256090676</td><td> 0.05898572</td></tr>\n",
       "\t<tr><td> 0.001362964</td><td>-0.317746855</td><td> 0.21374067</td></tr>\n",
       "\t<tr><td>-0.221400693</td><td> 0.120731486</td><td>-0.22201469</td></tr>\n",
       "\t<tr><td>-0.001450263</td><td> 0.420339649</td><td> 0.38288931</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 20 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t -0.009969788 & -0.121501078 & -0.20419401\\\\\n",
       "\t  0.186887139 & -0.046163013 &  0.13223387\\\\\n",
       "\t -0.101193522 & -0.141661215 & -0.37063341\\\\\n",
       "\t  0.060964112 & -0.346616669 &  0.03342558\\\\\n",
       "\t -0.512831098 & -0.458299483 &  0.44354554\\\\\n",
       "\t -0.077780541 &  0.094512914 & -0.23766491\\\\\n",
       "\t  0.003955674 &  0.254201102 &  0.25701898\\\\\n",
       "\t -0.016855040 & -0.127105942 & -0.34147617\\\\\n",
       "\t  0.203734347 &  0.196310283 & -0.00758741\\\\\n",
       "\t -0.104800666 &  0.208124774 & -0.11711820\\\\\n",
       "\t  0.113834968 & -0.016598895 & -0.09752299\\\\\n",
       "\t  0.063237343 &  0.213427257 &  0.21221151\\\\\n",
       "\t  0.043586465 & -0.008040409 &  0.01237648\\\\\n",
       "\t -0.082181602 &  0.055998387 &  0.10021686\\\\\n",
       "\t -0.094153311 &  0.228436101 & -0.04670258\\\\\n",
       "\t -0.173085857 &  0.047742282 & -0.20173015\\\\\n",
       "\t  0.718139369 & -0.256090676 &  0.05898572\\\\\n",
       "\t  0.001362964 & -0.317746855 &  0.21374067\\\\\n",
       "\t -0.221400693 &  0.120731486 & -0.22201469\\\\\n",
       "\t -0.001450263 &  0.420339649 &  0.38288931\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 20 × 3 of type dbl\n",
       "\n",
       "| -0.009969788 | -0.121501078 | -0.20419401 |\n",
       "|  0.186887139 | -0.046163013 |  0.13223387 |\n",
       "| -0.101193522 | -0.141661215 | -0.37063341 |\n",
       "|  0.060964112 | -0.346616669 |  0.03342558 |\n",
       "| -0.512831098 | -0.458299483 |  0.44354554 |\n",
       "| -0.077780541 |  0.094512914 | -0.23766491 |\n",
       "|  0.003955674 |  0.254201102 |  0.25701898 |\n",
       "| -0.016855040 | -0.127105942 | -0.34147617 |\n",
       "|  0.203734347 |  0.196310283 | -0.00758741 |\n",
       "| -0.104800666 |  0.208124774 | -0.11711820 |\n",
       "|  0.113834968 | -0.016598895 | -0.09752299 |\n",
       "|  0.063237343 |  0.213427257 |  0.21221151 |\n",
       "|  0.043586465 | -0.008040409 |  0.01237648 |\n",
       "| -0.082181602 |  0.055998387 |  0.10021686 |\n",
       "| -0.094153311 |  0.228436101 | -0.04670258 |\n",
       "| -0.173085857 |  0.047742282 | -0.20173015 |\n",
       "|  0.718139369 | -0.256090676 |  0.05898572 |\n",
       "|  0.001362964 | -0.317746855 |  0.21374067 |\n",
       "| -0.221400693 |  0.120731486 | -0.22201469 |\n",
       "| -0.001450263 |  0.420339649 |  0.38288931 |\n",
       "\n"
      ],
      "text/plain": [
       "      [,1]         [,2]         [,3]       \n",
       " [1,] -0.009969788 -0.121501078 -0.20419401\n",
       " [2,]  0.186887139 -0.046163013  0.13223387\n",
       " [3,] -0.101193522 -0.141661215 -0.37063341\n",
       " [4,]  0.060964112 -0.346616669  0.03342558\n",
       " [5,] -0.512831098 -0.458299483  0.44354554\n",
       " [6,] -0.077780541  0.094512914 -0.23766491\n",
       " [7,]  0.003955674  0.254201102  0.25701898\n",
       " [8,] -0.016855040 -0.127105942 -0.34147617\n",
       " [9,]  0.203734347  0.196310283 -0.00758741\n",
       "[10,] -0.104800666  0.208124774 -0.11711820\n",
       "[11,]  0.113834968 -0.016598895 -0.09752299\n",
       "[12,]  0.063237343  0.213427257  0.21221151\n",
       "[13,]  0.043586465 -0.008040409  0.01237648\n",
       "[14,] -0.082181602  0.055998387  0.10021686\n",
       "[15,] -0.094153311  0.228436101 -0.04670258\n",
       "[16,] -0.173085857  0.047742282 -0.20173015\n",
       "[17,]  0.718139369 -0.256090676  0.05898572\n",
       "[18,]  0.001362964 -0.317746855  0.21374067\n",
       "[19,] -0.221400693  0.120731486 -0.22201469\n",
       "[20,] -0.001450263  0.420339649  0.38288931"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 20 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>-0.02909460</td><td> 0.031027608</td><td> 0.344302062</td></tr>\n",
       "\t<tr><td> 0.23190170</td><td> 0.084158321</td><td>-0.403047146</td></tr>\n",
       "\t<tr><td>-0.12979237</td><td>-0.112030106</td><td>-0.133855684</td></tr>\n",
       "\t<tr><td> 0.09063830</td><td>-0.150034732</td><td>-0.059921010</td></tr>\n",
       "\t<tr><td>-0.39173848</td><td>-0.209788233</td><td>-0.008592976</td></tr>\n",
       "\t<tr><td>-0.11930102</td><td>-0.288113119</td><td>-0.480186091</td></tr>\n",
       "\t<tr><td>-0.22619839</td><td> 0.122191086</td><td>-0.006091381</td></tr>\n",
       "\t<tr><td> 0.21834490</td><td>-0.164740837</td><td>-0.074849953</td></tr>\n",
       "\t<tr><td> 0.26809619</td><td>-0.165185828</td><td> 0.003582504</td></tr>\n",
       "\t<tr><td>-0.38258341</td><td>-0.041647344</td><td> 0.042948559</td></tr>\n",
       "\t<tr><td> 0.21737727</td><td> 0.056375494</td><td> 0.277291769</td></tr>\n",
       "\t<tr><td> 0.01130349</td><td>-0.218167527</td><td>-0.264987331</td></tr>\n",
       "\t<tr><td> 0.16412985</td><td>-0.065834278</td><td> 0.157664098</td></tr>\n",
       "\t<tr><td> 0.03462910</td><td>-0.097067107</td><td> 0.157711712</td></tr>\n",
       "\t<tr><td> 0.05393456</td><td> 0.778658842</td><td>-0.283334468</td></tr>\n",
       "\t<tr><td>-0.15965387</td><td> 0.183746435</td><td> 0.008766141</td></tr>\n",
       "\t<tr><td> 0.43237930</td><td>-0.002016448</td><td> 0.080198839</td></tr>\n",
       "\t<tr><td>-0.12845980</td><td> 0.223805116</td><td> 0.055667431</td></tr>\n",
       "\t<tr><td>-0.31879992</td><td> 0.059073577</td><td> 0.277587462</td></tr>\n",
       "\t<tr><td> 0.16288721</td><td>-0.024410919</td><td> 0.309145462</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 20 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t -0.02909460 &  0.031027608 &  0.344302062\\\\\n",
       "\t  0.23190170 &  0.084158321 & -0.403047146\\\\\n",
       "\t -0.12979237 & -0.112030106 & -0.133855684\\\\\n",
       "\t  0.09063830 & -0.150034732 & -0.059921010\\\\\n",
       "\t -0.39173848 & -0.209788233 & -0.008592976\\\\\n",
       "\t -0.11930102 & -0.288113119 & -0.480186091\\\\\n",
       "\t -0.22619839 &  0.122191086 & -0.006091381\\\\\n",
       "\t  0.21834490 & -0.164740837 & -0.074849953\\\\\n",
       "\t  0.26809619 & -0.165185828 &  0.003582504\\\\\n",
       "\t -0.38258341 & -0.041647344 &  0.042948559\\\\\n",
       "\t  0.21737727 &  0.056375494 &  0.277291769\\\\\n",
       "\t  0.01130349 & -0.218167527 & -0.264987331\\\\\n",
       "\t  0.16412985 & -0.065834278 &  0.157664098\\\\\n",
       "\t  0.03462910 & -0.097067107 &  0.157711712\\\\\n",
       "\t  0.05393456 &  0.778658842 & -0.283334468\\\\\n",
       "\t -0.15965387 &  0.183746435 &  0.008766141\\\\\n",
       "\t  0.43237930 & -0.002016448 &  0.080198839\\\\\n",
       "\t -0.12845980 &  0.223805116 &  0.055667431\\\\\n",
       "\t -0.31879992 &  0.059073577 &  0.277587462\\\\\n",
       "\t  0.16288721 & -0.024410919 &  0.309145462\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 20 × 3 of type dbl\n",
       "\n",
       "| -0.02909460 |  0.031027608 |  0.344302062 |\n",
       "|  0.23190170 |  0.084158321 | -0.403047146 |\n",
       "| -0.12979237 | -0.112030106 | -0.133855684 |\n",
       "|  0.09063830 | -0.150034732 | -0.059921010 |\n",
       "| -0.39173848 | -0.209788233 | -0.008592976 |\n",
       "| -0.11930102 | -0.288113119 | -0.480186091 |\n",
       "| -0.22619839 |  0.122191086 | -0.006091381 |\n",
       "|  0.21834490 | -0.164740837 | -0.074849953 |\n",
       "|  0.26809619 | -0.165185828 |  0.003582504 |\n",
       "| -0.38258341 | -0.041647344 |  0.042948559 |\n",
       "|  0.21737727 |  0.056375494 |  0.277291769 |\n",
       "|  0.01130349 | -0.218167527 | -0.264987331 |\n",
       "|  0.16412985 | -0.065834278 |  0.157664098 |\n",
       "|  0.03462910 | -0.097067107 |  0.157711712 |\n",
       "|  0.05393456 |  0.778658842 | -0.283334468 |\n",
       "| -0.15965387 |  0.183746435 |  0.008766141 |\n",
       "|  0.43237930 | -0.002016448 |  0.080198839 |\n",
       "| -0.12845980 |  0.223805116 |  0.055667431 |\n",
       "| -0.31879992 |  0.059073577 |  0.277587462 |\n",
       "|  0.16288721 | -0.024410919 |  0.309145462 |\n",
       "\n"
      ],
      "text/plain": [
       "      [,1]        [,2]         [,3]        \n",
       " [1,] -0.02909460  0.031027608  0.344302062\n",
       " [2,]  0.23190170  0.084158321 -0.403047146\n",
       " [3,] -0.12979237 -0.112030106 -0.133855684\n",
       " [4,]  0.09063830 -0.150034732 -0.059921010\n",
       " [5,] -0.39173848 -0.209788233 -0.008592976\n",
       " [6,] -0.11930102 -0.288113119 -0.480186091\n",
       " [7,] -0.22619839  0.122191086 -0.006091381\n",
       " [8,]  0.21834490 -0.164740837 -0.074849953\n",
       " [9,]  0.26809619 -0.165185828  0.003582504\n",
       "[10,] -0.38258341 -0.041647344  0.042948559\n",
       "[11,]  0.21737727  0.056375494  0.277291769\n",
       "[12,]  0.01130349 -0.218167527 -0.264987331\n",
       "[13,]  0.16412985 -0.065834278  0.157664098\n",
       "[14,]  0.03462910 -0.097067107  0.157711712\n",
       "[15,]  0.05393456  0.778658842 -0.283334468\n",
       "[16,] -0.15965387  0.183746435  0.008766141\n",
       "[17,]  0.43237930 -0.002016448  0.080198839\n",
       "[18,] -0.12845980  0.223805116  0.055667431\n",
       "[19,] -0.31879992  0.059073577  0.277587462\n",
       "[20,]  0.16288721 -0.024410919  0.309145462"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JxHImTuIUGEkCBASBAgJAgQEgQICQKE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\nQEgQICQIEBIECAkChAQB/wOtx2zFtzyrgQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test<-data.frame(\n",
    "  X1=c(191, 193, 189, 211, 176, 169, 154, 193, 176, 156, \n",
    "       189, 162, 182, 167, 154, 166, 247, 202, 157, 138), \n",
    "  X2=c(36, 38, 35, 38, 31, 34, 34, 36, 37, 33, \n",
    "       37, 35, 36, 34, 33, 33, 46, 37, 32, 33),\n",
    "  X3=c(50, 58, 46, 56, 74, 50, 64, 46, 54, 54,\n",
    "       52, 62, 56, 60, 56, 52, 50, 62, 52, 68), \n",
    "  Y1=c( 5, 12, 13,  8, 15, 17, 14,  6,  4, 15, \n",
    "        2, 12,  4,  6, 17, 13,  1, 12, 11,  2), \n",
    "  Y2=c(162, 101, 155, 101, 200, 120, 215,  70,  60, 225, \n",
    "       110, 105, 101, 125, 251, 210,  50, 210, 230, 110), \n",
    "  Y3=c(60, 101, 58, 38, 40, 38, 105, 31, 25, 73, \n",
    "       60, 37, 42, 40, 250, 115, 50, 120, 80, 43)\n",
    ")\n",
    "test<-scale(test)\n",
    "\n",
    "ca<-cancor(test[,1:3],test[,4:6]); ca\n",
    "\n",
    "U<-as.matrix(test[, 1:3])%*% ca$xcoef ; U\n",
    "V<-as.matrix(test[, 4:6])%*% ca$ycoef ; V\n",
    "\n",
    "opar <- par(mfrow = c(1, 1),mar = c(5,4,1,1))\n",
    "\n",
    "plot(U[,1], V[,1], xlab=\"U1\", ylab=\"V1\")\n",
    "plot(U[,3], V[,3], xlab=\"U3\", ylab=\"V3\")\n",
    "\n",
    "par(opar)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.0.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
